14,572 research outputs found

    Robust Multidimensional Poverty Comparisons

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    We investigate how to make poverty comparisons using multidimensional indicators of well-being, showing in particular how to check whether the comparisons are robust to the choice of poverty indices and poverty lines. Our methodology applies equally well to either of what can be defined as "union" and "intersection" approaches to dealing with multidimensional indicators of well-being. When one of two variables is discrete, our methods specialize to those that Atkinson (1991), Jenkins and Lambert (1993) and others have developed to deal with household composition heterogeneity. The results also extend the statistical results recently derived in Davidson and Duclos (2000) to cases where well-being is measured in two or more dimensions. We thus derive the sampling distribution of various multidimensional poverty estimators, including estimators of the "critical" frontiers of poverty lines above which multidimensional poverty comparisons are no longer ethically robust.Multidimensional Poverty, Stochastic Dominance

    Polarization: Robust Multidimensional Poverty Comparisons

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    We investigate how to make poverty comparisons using multidimensional indicators of well-being, showing in particular how to check whether the comparisons are robust to aggregation procedures and to the choice of multidimensional poverty lines. In contrast to earlier work, our methodology applies equally well to what can be defined as "union", "intersection" or "intermediate" approaches to dealing with multidimensional indicators of well-being. When one of two indicators is discrete, our methods specialize to those that have previously been developed to deal with household composition heterogeneity. To make these procedures of some practical usefulness, the paper is also the first to derive the sampling distribution of various multidimensional poverty estimators, including estimators of the "critical" poverty frontiers outside which multidimensional poverty comparisons can no longer be deemed ethically robust. The results are illustrated using data from a number of developing countries.Multidimensional Poverty, Stochastic Dominance

    Fast and robust curve skeletonization for real-world elongated objects

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    We consider the problem of extracting curve skeletons of three-dimensional, elongated objects given a noisy surface, which has applications in agricultural contexts such as extracting the branching structure of plants. We describe an efficient and robust method based on breadth-first search that can determine curve skeletons in these contexts. Our approach is capable of automatically detecting junction points as well as spurious segments and loops. All of that is accomplished with only one user-adjustable parameter. The run time of our method ranges from hundreds of milliseconds to less than four seconds on large, challenging datasets, which makes it appropriate for situations where real-time decision making is needed. Experiments on synthetic models as well as on data from real world objects, some of which were collected in challenging field conditions, show that our approach compares favorably to classical thinning algorithms as well as to recent contributions to the field.Comment: 47 pages; IEEE WACV 2018, main paper and supplementary materia

    On multivariate quantiles under partial orders

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    This paper focuses on generalizing quantiles from the ordering point of view. We propose the concept of partial quantiles, which are based on a given partial order. We establish that partial quantiles are equivariant under order-preserving transformations of the data, robust to outliers, characterize the probability distribution if the partial order is sufficiently rich, generalize the concept of efficient frontier, and can measure dispersion from the partial order perspective. We also study several statistical aspects of partial quantiles. We provide estimators, associated rates of convergence, and asymptotic distributions that hold uniformly over a continuum of quantile indices. Furthermore, we provide procedures that can restore monotonicity properties that might have been disturbed by estimation error, establish computational complexity bounds, and point out a concentration of measure phenomenon (the latter under independence and the componentwise natural order). Finally, we illustrate the concepts by discussing several theoretical examples and simulations. Empirical applications to compare intake nutrients within diets, to evaluate the performance of investment funds, and to study the impact of policies on tobacco awareness are also presented to illustrate the concepts and their use.Comment: Published in at http://dx.doi.org/10.1214/10-AOS863 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Discrete Symmetries in the Weyl Expansion for Quantum Billiards

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    We consider two and three-dimensional quantum billiards with discrete symmetries. We derive the first terms of the Weyl expansion for the level density projected onto the irreducible representations of the symmetry group. As an illustration the method is applied to the icosahedral billiard. The paper was published in J. Phys. A /27/ (1994) 4317-4323Comment: 8 printed pages Latex fil
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